Description:
The first five chapters display topological aspects of qualitative analysis, stability theory, bifurcation theory, classical and singular perturbation theory and application to synchronization theory of weakly coupled oscillators. Each chapters is supplemented by a list of commented exercices which allow gradual initiation to models. Chapter VI deals with stationary waves and discusses the relation with qualitative analysis. The last chapter is concerned with Hodgkin-Huxley approaches and focuses on two aspects. One is about synchronization of cardiac cells in the sinusal node and the other is on bursting oscillations.
Review Quotes:
From the reviews of the first edition:
"This book deals with continuous dynamical system theory, from the point of view of qualitative methods related to nonlinear differential equations and their applications. ... This book has the interest to be a 'user's guide' to tackle the very large field of qualitative methods of nonlinear dynamics." (Christian Mira, Zentralblatt MATH, Vol. 1080, 2006)